Teaching my son the multiplication tables

I am teaching my son the multiplication tables in a Trachtenberg kind of way.
The tables until 6 are easy for him. We are now training to do 8-12.
7 is the most difficult for him (as it is for many kids).

We have already done ‘sequences’ for about two years. I started doing those from when they were 3-4 years old.
A sequence is 2, 4, 6, 8, …
Or 3, 6, 9, 12, …
Or 7, 14, 21,…
etc.
My youngest is 5 and with her I only do the sequences.

My oldest is now learning the tables at school.
What I do for numbers close to 10 (8 - 12) is this.
I have him first add a zero to the number (multiplication by 10) and then add or subtract the number or twice the number.

11 = 10 + 1, so:
1 * 11 = 10 + 1 = 11
2 * 11 = 20 + 2 = 22
3 * 11 = 30 + 3 = 33
4 * 11 = 40 + 4 = 44
5 * 11 = 50 + 5 = 55
6 * 11 = 60 + 6 = 66
7 * 11 = 70 + 7 = 77
8 * 11 = 80 + 8 = 88
9 * 11 = 90 + 9 = 99
10 * 11 = 100 + 10 = 110
11 * 11 = 110 + 11 = 121
12 * 11 = 120 + 12 = 132

9 = 10 - 1, so:
1 * 9 = 10 - 1 = 9
2 * 9 = 20 - 2 = 18
3 * 9 = 30 - 3 = 27
4 * 9 = 40 - 4 = 36
5 * 9 = 50 - 5 = 45
6 * 9 = 60 - 6 = 54
7 * 9 = 70 - 7 = 63
8 * 9 = 80 - 8 = 72
9 * 9 = 90 - 9 = 81
10 * 9 = 100 - 10 = 90
11 * 9 = 110 - 11 = 99
12 * 9 = 120 - 12 = 108

12 = 10 + 2, so:
1 * 12 = 10 + 2 = 12
2 * 12 = 20 + 4 = 24
3 * 12 = 30 + 6 = 36
4 * 12 = 40 + 8 = 48
5 * 12 = 50 + 10 = 60
6 * 12 = 60 + 12 = 72
7 * 12 = 70 + 14 = 84
8 * 12 = 80 + 16 = 96
9 * 12 = 90 + 18 = 108
10 * 12 = 100 + 20 = 120
11 * 12 = 110 + 22 = 132
12 * 12 = 120 + 24 = 144

8 = 10 - 2, so:
1 * 8 = 10 - 2 = 8
2 * 8 = 20 - 4 = 16
3 * 8 = 30 - 6 = 24
4 * 8 = 40 - 8 = 32
5 * 8 = 50 - 10 = 40
6 * 8 = 60 - 12 = 48
7 * 8 = 70 - 14 = 56
8 * 8 = 80 - 16 = 64
9 * 8 = 90 - 18 = 72
10 * 8 = 100 - 20 = 80
11 * 8 = 110 - 22 = 88
12 * 8 = 120 - 24 = 96

We have not yet done a lot with the 7 table.
We do the 7 sequence from time to time.
For the table I plan to use the following.

He is quick to halve.
7 is 5 + 2. 5 is halve of ten and 2 is double of one.
So I call it ’ halve and double’. There is a shift between halve and double, but ‘halve and double’ just sounds better.

In the case of 4 (times 7), we do halve of 4 (2) and double 4 (8).
I have him picture the 2 next to the 8 to form 28.
In the case of 8, again we do halve of 8 (4) and double (16).
He knows by then he needs to concatenate them, effectively picturing 4|16 = 56. Or he can just do 40+16.

Btw, I don’t force him to do anything. I just show him options.
Until now he just picks them up easily.

For even numbers ‘halve plus double’ is easy:
2 * 7 = 1|4 = 14
4 * 7 = 2|8 = 28
6 * 7 = 3|12 = 42
8 * 7 = 4|16 = 56
10 * 7 = 5|20 = 70
12 * 7 = 6|24 = 84

For odd numbers I just have him get the next number in the sequence.

Either that or have him multiply the number by 10, halve and then double:
1 * 7 = 5 + 2 = 7
2 * 7 = 10 + 4 = 14
3 * 7 = 15 + 6 = 21
4 * 7 = 20 + 8 = 28
5 * 7 = 25 + 10 = 35
6 * 7 = 30 + 12 = 42
7 * 7 = 35 + 14 = 49
8 * 7 = 40 + 16 = 56
9 * 7 = 45 + 18 = 63
10 * 7 = 50 + 20 = 70
11 * 7 = 55 + 22 = 77
12 * 7 = 60 + 24 = 84

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8 posts were split to a new topic: Trachtenberg and Arthur Benjamin Method

I like this. I also taught both my sons, 6 and 7, their tables when they were 5 and 6. I used the Major system and they learned them over about a month. They have no problems with recall.

eg. 12 x9 = Tune Up using Adhesive = 108.

easy peasy…